10/09/2008 @ 6:20PM

Can Math Cure Cancer?

In her laboratory at the University of Washington, mathematician Kristin Rae Swanson peers into the future of brain cancer patients–on her computer screen. She has created a software program that uses data from magnetic resonance imaging scans to simulate how fast a patient’s brain tumor is likely to spread. She can pinpoint with uncanny precision where a tumor will grow months ahead of time and predict how long a patient is likely to live under various treatment scenarios.

She first proposed the idea ten years ago and “was laughed out of the room” by skeptical doctors who figured brain tumor growth was too erratic to predict, Swanson says. But she has developed an equation that takes into account how fast tumors divide and disperse through brain tissue and can predict their path. It takes three hours on a PC to run a patient’s data through this simulation. She has found that her model is accurate in predicting cancer progression in 350 patients, including 30 still undergoing treatment.

Swanson, who was inspired to go into cancer research after her father died of lung cancer, hopes her simulation will lead to a new generation of customized brain cancer treatments. Right now brain glioblastoma patients typically get once-daily radiation for six weeks. But her computer model predicts that some slow-growing tumors could be treated just as well with less-frequent radiation, sparing patients bad side effects. Others with fast-proliferating tumors would live longer with smaller doses of radiation two or three times a day. A human trial with customized radiation therapy could begin next year.

Swanson is among a handful of mathematicians and engineers trying to bring new precision to the crude science of cancer treatment. Their audacious aim is to make something like a weather forecast for cancer, inputting scan data, pathology scores or gene test results into equations and calculating where and at what rate a patient’s tumor is likely to spread. The techniques come from fields such as evolutionary biology, chemical engineering and physics to capture tumor complexity in a few well-considered equations. Swanson’s bears a certain resemblance to the Fourier heat equation.

“People get data from weather satellites and balloons, feed them into a model and get a prediction of what will happen. There is no reason why you shouldn’t be able to do something like that with tumors,” says Vanderbilt University cancer researcher Vito Quaranta. Cancer forecasting may have an even brighter future than climate models, since doctors can validate their models on real patients, a luxury climatologists don’t have. Cancer research “is a little like physics before Isaac Newton,” says evolutionary biologist Franziska Michor at Memorial Sloan-Kettering Cancer Center, who has devised a model of how leukemia cells respond to the drug Gleevec. “We are trying to make it into a predictive, quantitative science.”

The goal is to replace today’s one-size-fits-all therapies with personalized treatment, maximizing efficacy and minimizing side effects. Progress on this front has been slow. One reason is the sheer number of mutations involved. A recent Johns Hopkins University study found 1,007 different gene alterations involved in pancreatic cancers. Tumor growth is also affected by blood supply, nutrient availability and the immune system.

“There has been an implicit assumption that if we just generated enough gene data it would coalesce magically into a complete understanding of cancer,” says H. Lee Moffitt Cancer Center radiologist Robert Gatenby. When he started using math to study tumor spread in 1990s, colleagues “alternated between sarcasm and open mocking.” One reviewer called him lazy. Now there is more data than biologists can handle.

The field is in its infancy, but researchers at some of the biggest cancer centers are starting to get involved. The National Cancer Institute spends a modest $11 million annually on virtual tumor work, up from almost nothing a few years ago. Biotech firms such as Gene Network Sciences are pursuing the concept. “It can have a massive impact,” says Moffitt cancer modeler Alexander Anderson.

The fancy math models may help drug developers sort through tumor-promoting proteins faster to find which drug combinations might work best on which patients. There are dozens of targeted drugs in testing, but each may work only on subsets of patients with certain gene alterations. “We desperately need a method to distinguish which mutations are driving the tumor’s growth and which are mere hitchhikers,” says Sloan-Kettering’s Michor.

Another goal of the research is to improve the results of existing treatments. In Houston, University of Texas chemical engineer Vittorio Cristini and M.D. Anderson pathologist Mary Elizabeth Edgerton are creating a simulation that predicts the location of cancer deposits that cannot be seen on mammography. The goal is to come up with mapping software that could help breast surgeons get all the cancer out the first time; up to 50% of early breast cancer patients now need repeat operations. Cristini and Edgerton send data to a University of Texas at Austin center that can handle 62 trillion calculations per second. Even so, it can take a day to run the virtual experiment.

Radiologist Robert Gatenby has used a branch of mathematics known as catastrophe theory, previously used to study things like bridge collapses, to examine why tumors often come roaring back after first responding to chemotherapy. His early results suggest that in advanced cases blasting the tumor with too much chemo can backfire by allowing resistant cells to take over and kill the patient faster. A better idea, his model predicts, is to use just enough chemo to keep a small population of drug-sensitive tumor cells around that will block the spread of resistant cells. So far he has been able to keep mice with otherwise fatal ovarian tumors alive indefinitely by using progressively lower doses of carboplatin. The harder part will be convincing colleagues that such a radical idea is worth testing on people.

Computers and math could also help design new cancer vaccines, says Stanford University hematologist Peter P. Lee. With University of Maryland mathematician Doron Levy, he has been studying why the immune system can’t wipe out leukemia cells that are missed by the breakthrough drug Gleevec. Patients must remain on this drug indefinitely, and some develop resistance. Plugging data from patient blood samples into a computer revealed a likely reason: Gleevec wipes out cancer so fast that any immune system response also fizzles out before all the leukemia cells are dead.

But the calculations revealed that a simple vaccine given at precisely the right time could bolster the immune system. The vaccine would consist of dead leukemia cells from the patients’ own blood. Lee suspects that one reason other cancer vaccines have failed is that researchers ignored such timing considerations. Human trials of the vaccine could start next year. “Naysayers say: ‘Talk to me when you have cured patients,’” he says. “We are trying to do that.”

Mathematical models are only as good as the data and assumptions that go into them. Their predictions will need to be validated against results from hundreds of cancer patients. “It will definitely guide how we treat patients,” says
Sanofi-Aventis
cancer research head Christoph Lengauer. But so far, too many of the results “are irrelevant or obvious.”

Virtual tumors will get more realistic, enough to make specific predictions that can be tested. “This is the moment of truth,” says Cristini. “The next five years will tell us if this field will be one of the biggest revolutions in science or a flop.”